Results 101 to 110 of about 855 (128)

Initial value problem for fractional evolution equations [PDF]

, 2012
Hongxia Fan, Jia Mu
core   +1 more source

Study on the existence of solutions for a generalized functional integral equation in spaces [PDF]

core   +1 more source

A Measure of Weak Noncompactness in $$L^1({\mathbb {R}}^N)$$ and Applications

Mediterranean Journal of Mathematics, 2022
A new measure of weak noncompactness in the Banach space \(L^1(\mathbb{R}^N)\) is proposed. It is a generalization of the Banas-Knap measure of weak noncompactness, which in turn is a generalization of the De Blasi measure of weak noncompactness. Then, the multidimensional nonlinear functional integral equation \[ u(t,x)=f(t,x,u(t,x))+ g\left( t,x ...
Bilal Boulfoul, Smaïl Djebali
exaly   +5 more sources

Existence of fixed points and measures of weak noncompactness

Nonlinear Analysis: Theory, Methods & Applications, 2009
The author proves the existence of fixed points of an operator \(A\) which is defined on a closed convex subset \(M\) of a Banach space \(X\) into itself and satisfies the following properties: (a) the measure of weak noncompactness of \(A(C)\) where \(C\subset M\) is not relatively weakly compact is strictly less than the measure of weak compactness ...
Jesús Garcı́a-Falset
exaly   +4 more sources

Weakly demicompact linear operators and axiomatic measures of weak noncompactness

Mathematica Slovaca, 2019
Abstract In this paper, we study the relationship between the class of weakly demicompact linear operators, introduced in [KRICHEN, B.—O’REGAN, D.: On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), 625–630], and measures of weak noncompactness of linear operators with respect to an axiomatic one. Moreover,
Bilel Krichen, Donal O’Regan
exaly   +4 more sources

Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the lebesgue space

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author shows that, for a subset \(X\) of \(L_1\) which is compact in measure, the continuity, demicontinuity, and weak sequential continuity of \(T: X\to X\) are equivalent. This makes it possible to enlarge the applicability of fixed point theorems involving weakly condensing operators.
Józef Banaś
exaly   +5 more sources

Stability of relative essential spectra of the transport operator in $$L^1$$-space by means of measures of noncompactness and relative weak demicompactness

Monatshefte für Mathematik, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Slim Chelly, Aref Jeribi, Bilel Krichen
openalex   +3 more sources

Measures of Weak Noncompactness and Fixed Points

, 2017
The interaction between measures of weak noncompactness and fixed point theory is really strong and fruitful. In particular, measures of weak noncompactness play a significant role in topological fixed point problems. The purpose of this chapter is to exhibit the importance of the use of measures of weak noncompactness in topological fixed point theory
Agnieszka Chlebowicz, Mohamed-Aziz Taoudi   +1 more
openalex   +2 more sources

Measure of super weak noncompactness in some Banach sequence spaces

Journal of Mathematical Analysis and Applications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kun Tu
openalex   +3 more sources

Convexification of super weakly compact sets and measure of super weak noncompactness

Proceedings of the American Mathematical Society, 2020
Let \(A\) be a subset of a Banach space \(X\), and let \(\textrm{co}(A)\) and \(\textrm{aff}(A)\) denote the convex hull and the affine hull of \(A\). We say that a subset \(B\) of a Banach space \(Y\) is \textit{finitely representable in \(A\)} if for every finite subset \(B_0\) of \(B\) and \(r>1\) there is a finite subset \(A_0\) of \(A\) and an ...
Kun Tu
openalex   +3 more sources